Given Wall Street's reaction, it appears that investors are betting that BP (BP) will get away with paying a nominal sum. The company's shares recovered in Friday's trading after one financial analyst estimated that the disaster could cost the company as little as $3 billion. (O.K., $3 billion isn't insignificant, but for a company that raked in a $6.1 billion profit in a three-month period, it basically amounts to a minor setback.)

"I can tell you this: It's going to cost them multibillions of dollars. Anywhere from $10 billion to $15 billion," says Daniel Becnel, who filed the first class action against BP and others on behalf of Louisiana shrimpers, fisherman and commercial boaters on Thursday. "We're getting calls at the rate of 200 an hour. People say they're nauseated and have throat irritation. That class is probably going to include 1 million people."

Another attorney, Jerrold Parker, of Parker Waichman Alonso, who has worked on cases concerning another oil spill around New Orleans, thinks the disaster could be "catastrophic."

"Exxon Valdez cost $4 billion or $5 billion dollars -- this could be bigger than that," says Parker. "You've got fisherman who are out of work. Oil workers who can no longer work on the rigs because of the danger of fire. How about tourists on cruise ships that can't port? Or taxi drivers who aren't giving rides? The devastation to the New Orleans area is going to be incredible."

Lessons From Exxon Valdez

But in past cases, corporations have been able to talk their way out of hefty damages. In the case of the Exxon Valdez oil spill of 1989, for example, Exxon spent more than a decade weaseling its way out of paying $5 billion in punitive damages to plaintiffs, which included more than 34,000 fishermen, natives, local governments, etc.

Exxon appealed a 1994 verdict in which an Anchorage jury awarded $5 billion in punitive damages to the plaintiffs; the damages were then halved to $2.5 billion. Then the company appealed to the Supreme Court, which capped damages at a little more than $500 million. (The Ninth Circuit Court of Appeals later ruled that the company was still obligated to pay $470 million for interest on the damages.)

BP claims it intends to pay for all rightful damages resulting from the spill: "We are taking full responsibility for the spill and we will clean it up and where people can present legitimate claims for damages we will honor them. We are going to be very, very aggressive in all of that," BP chief executive Tony Hayward told Reuters on Friday. Still, the company doesn't have the cleanest track record.

After the company was fined $87 million by the Occupational Safety and Health Administration for failing to correct hazardous practices related to a 2005 chemical explosion in Texas City, BP contested the fines. The company also appealed $100 million in damages which were awarded to 10 employees as a result of the chemical release. (Last month a federal judge overturned that verdict.)